Results 1 
9 of
9
Probabilistic Default Reasoning with Conditional Constraints
 ANN. MATH. ARTIF. INTELL
, 2000
"... We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of , lexicographic, ..."
Abstract

Cited by 35 (20 self)
 Add to MetaCart
We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of , lexicographic, and conditional entailment for conditional constraints, which are probabilistic generalizations of Pearl's entailment in system , Lehmann's lexicographic entailment, and Geffner's conditional entailment, respectively. We show that the new formalisms have nice properties. In particular, they show a similar behavior as referenceclass reasoning in a number of uncontroversial examples. The new formalisms, however, also avoid many drawbacks of referenceclass reasoning. More precisely, they can handle complex scenarios and even purely probabilistic subjective knowledge as input. Moreover, conclusions are drawn in a global way from all the available knowledge as a whole. We then show that the new formalisms also have nice general nonmonotonic properties. In detail, the new notions of , lexicographic, and conditional entailment have similar properties as their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of  and lexicographic entailment satisfy the property of rational monotonicity. Furthermore, the new notions of , lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints. Finally, we provide algorithms for reasoning under the new formalisms, and we analyze its computational com...
Answering Queries from Statistics and Probabilistic Views
, 2005
"... this paper, require complex correlations between tuples, for which the query semantics has not been previously studied ..."
Abstract

Cited by 34 (3 self)
 Add to MetaCart
this paper, require complex correlations between tuples, for which the query semantics has not been previously studied
Materialized views in probabilistic databases for information exchange and query optimization
 IN PROCEEDINGS OF VLDB
, 2007
"... Views over probabilistic data contain correlations between tuples, and the current approach is to capture these correlations using explicit lineage. In this paper we propose an alternative approach to materializing probabilistic views, by giving conditions under which a view can be represented by a ..."
Abstract

Cited by 27 (9 self)
 Add to MetaCart
Views over probabilistic data contain correlations between tuples, and the current approach is to capture these correlations using explicit lineage. In this paper we propose an alternative approach to materializing probabilistic views, by giving conditions under which a view can be represented by a blockindependent disjoint (BID) table. Not all views can be represented as BID tables and so we propose a novel partial representation that can represent all views but may not define a unique probability distribution. We then give conditions on when a query’s value on a partial representation will be uniquely defined. We apply our theory to two applications: query processing using views and information exchange using views. In query processing on probabilistic data, we can ignore the lineage and use materialized views to more efficiently answer queries. By contrast, if the view has explicit lineage, the query evaluation must reprocess the lineage to compute the query resulting in dramatically slower execution. The second application is information exchange when we do not wish to disclose the entire lineage, which otherwise may result in shipping the entire database. The paper contains several theoretical results that completely solve the problem of deciding whether a conjunctive view can be represented as a BID and whether a query on a partial representation is uniquely determined. We validate our approach experimentally showing that representable views exist in real and synthetic workloads and show over three magnitudes of improvement in query processing versus a lineage based approach.
Probability Update: Conditioning vs. CrossEntropy
 In Proc. Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI
, 1997
"... Conditioning is the generally agreedupon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of crossentropy minimization, to handle updates that involve uncertain information. In thi ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
Conditioning is the generally agreedupon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of crossentropy minimization, to handle updates that involve uncertain information. In this paper we reexamine such a case: van Fraassen's Judy Benjamin problem [1987], which in essence asks how one might update given the value of a conditional probability. We argue thatcontrary to the suggestions in the literatureit is possible to use simple conditionalization in this case, and thereby obtain answers that agree fully with intuition. This contrasts with proposals such as crossentropy, which are easier to apply but can give unsatisfactory answers. Based on the lessons from this example, we speculate on some general philosophical issues concerning probability update. 1 INTRODUCTION How should one update one's beliefs, represented as a probability distribution Pr over some ...
Maximum entropy probabilistic logic
, 2002
"... Recent research has shown there are two types of uncertainty that can be expressed in firstorder logic— propositional and statistical uncertainty—and that both types can be represented in terms of probability spaces. However, these efforts have fallen short of providing a general account of how to ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
Recent research has shown there are two types of uncertainty that can be expressed in firstorder logic— propositional and statistical uncertainty—and that both types can be represented in terms of probability spaces. However, these efforts have fallen short of providing a general account of how to design probability measures for these spaces; as a result, we lack a crucial component of any system that reasons under these types of uncertainty. In this paper, we describe an automatic procedure for defining such measures in terms of a probabilistic knowledge base. In particular, we employ the principle of maximum entropy to select measures that are consistent with our knowledge and that make the fewest assumptions in doing so. This approach yields models of firstorder uncertainty that are principled, intuitive, and economical in their representation.
Minimum CrossEntropy Reasoning: A Statistical Justification
 Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI95
, 1995
"... Degrees of belief are formed using observed evidence and statistical background information. In this paper we examine the process of how prior degrees of belief derived from the evidence are combined with statistical data to form more specific degrees of belief. A statistical model for this process ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
Degrees of belief are formed using observed evidence and statistical background information. In this paper we examine the process of how prior degrees of belief derived from the evidence are combined with statistical data to form more specific degrees of belief. A statistical model for this process then is shown to vindicate the crossentropy minimization principle as a rule for probabilistic defaultinference. 1 Introduction A knowledge based system incorporating reasoning with uncertain information gives rise to quantitative statements of two different kinds: statements expressing statistical information and statements of degrees of belief. "10% of applicants seeking employment at company X who are invited to an interview will get a job there" is a statistical statement. "The likelihood that I will be invited for an interview if I apply for a job at company X is about 0.6" expresses a degree of belief. In this paper, both of these kinds of statements are regarded as probabilistic, i...
Applications of probabilistic constraints
, 2007
"... Relational database systems are a successful platform to manage large amounts of data, but do not cope well with uncertainty. However, the amount of uncertain data is growing at an unprecedented rate from both traditional sources (e.g. integrating enterprise data) and from next generation sources (e ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Relational database systems are a successful platform to manage large amounts of data, but do not cope well with uncertainty. However, the amount of uncertain data is growing at an unprecedented rate from both traditional sources (e.g. integrating enterprise data) and from next generation sources (e.g. information extraction). This trend has prompted the database community to investigate a promising new technique, probabilistic databases, that natively handle uncertainty. In this nascent area, it is an open question which techniques from traditional database management apply. A remarkably useful technique in standard relational databases is to allow users to enrich the semantics of their data by declaring constraints. Two traditional uses of constraints are to prevent errors while updating the data and to optimize queries. More recently, constraints provided an elegant solution to the problem of data exchange. These successes give us reason to believe that constraints will play a large role in the theory and implementation of probabilistic databases. This report proposes to generalize constraints to handle uncertainty in the data and the constraints themselves. We identify several traditional and emerging applications that are naturally modeled with probabilistic constraints. 1 1
Maximum Entropy Probabilistic Logic
"... Recent research has shown there are two types of uncertainty that can be expressed in firstorder logic propositional and statistical uncertaintyand that both types can be represented in terms of probability spaces. ..."
Abstract
 Add to MetaCart
Recent research has shown there are two types of uncertainty that can be expressed in firstorder logic propositional and statistical uncertaintyand that both types can be represented in terms of probability spaces.